The present invention relates to a surface acoustic wave device and a piezoelectric substrate used therefor.
In recent years, various kinds of mobile communication terminal devices, including cellular telephones, have come into widespread use. It is highly desirable to reduce this kind of terminal equipment in size and weight for enhanced portability. In order to reduce the size and weight of terminal devices, their electronic parts must be substantially reduced in size and weight. For this reason, surface acoustic wave devices enabling size and weight reduction, namely, surface acoustic wave filters, are often used for high- and intermediate-frequency parts of terminal devices. Such devices are formed with an inter-digital electrode for exciting, receiving, reflecting and propagating surface acoustic waves on the surface of a piezoelectric substrate thereof.
Among characteristics important to a piezoelectric substrate used for surface acoustic wave devices are surface wave velocity (SAW velocity), temperature coefficient of center frequency in the case of filters or of resonant frequency in the case of resonators (the temperature coefficient of frequency: TCF), and electromechanical coupling factor (k2). The characteristics of typical piezoelectric substrates currently known for surface acoustic wave devices are set forth below in Table 1. For details regarding these characteristics, reference should be made to Yasutaka SHIMIZU, xe2x80x9cPropagation characteristics of SAW materials and their current applicationxe2x80x9d, the Transactions of The Institute of Electronics, Information and Communication Engineers A, Vol. J76-A, No.2, pp. 129-137 (1993). Hereinafter, the piezoelectric substrates for surface acoustic wave devices are referred to using the designations in Table 1.
As can be seen from Table 1, currently known piezoelectric substrates are divided into the group including 128LN, 64LN, and 36LT which have high SAW velocities and high electromechanical coupling factor and the group including LT112 and ST quartz crystal which have low SAW velocities and low electromechanical coupling factor. The piezoelectric substrates which belong to the group with high SAW velocity and high electromechanical coupling factor (128LN, 64LN, and 36LT) are used for surface acoustic wave filters of high-frequency parts of terminal devices. The piezoelectric substrates which belong to the group with low SAW velocity and low electromechanical coupling factor (LT112 and ST quartz crystal) are used for surface acoustic wave filters of intermediate-frequency parts of terminal devices.
Various systems are practically employed all over the world for mobile communications devices, typically cellular telephones, and are all used at frequencies of the order of 1 GHz. Therefore, filters used for high-frequency parts of terminal devices have a center frequency of approximately 1 GHz. A surface acoustic wave filter has a center frequency substantially proportional to the SAW velocity of the piezoelectric substrate used and almost inversely proportional to the width of electrode fingers formed on the substrate. To enable such filters to be operated at high frequencies, therefore, it is preferable to utilize substrates having high SAW velocities, for instance, 128LN, 64LN, and 36LT. Also, a wide passband width of 20 MHz or more is required for filters used as high-frequency parts. To achieve such wide passband, however, it is essential for the piezoelectric substrate to have a large electromechanical coupling factor k2. For these reasons, much use is made of 128LN, 64LN, and 36LT.
On the other hand, mobile communication terminal devices use an intermediate frequency in the 70 to 300 MHz band. When a filter having a center frequency in this frequency band is constructed using a surface acoustic wave device, if the aforementioned 128LN, 64LN, or 36 LT is used as the piezoelectric substrate, the widths of the electrode fingers formed on the substrate have to be much larger than those of the aforementioned filter used as a high-frequency part.
More specifically, the following equation (1) roughly applies to the relationship among the width d of an electrode finger of a surface acoustic wave transducer that forms a surface acoustic wave filter, the center frequency f0 of the surface acoustic wave filter, and the SAW velocity V of the piezoelectric substrate used.
f0=V/(4d)xe2x80x83xe2x80x83(1) 
If a surface acoustic wave filter having a center frequency of 1 GHz is constructed on the assumption that the SAW velocity is 4000 m/s, the width of the electrode finger thereof is calculated from the equation (1) to be
d=4000(m/s)/(4xc3x971000(MHz))=1 xcexcm 
On the other hand, when an intermediate-frequency filter having a center frequency of 100 MHz is constructed using this piezoelectric substrate having a SAW velocity of 4000 m/s, the width of the electrode finger required for this is given by
d=4000(m/s)/(4xc3x97100(MHz))=10 xcexcm 
Thus, the required width of the electrode finger is ten times as large as that for the high-frequency part filter. A large width of the electrode finger means that the surface acoustic wave intermediate-frequency filter itself becomes large. Therefore, in order to make a surface acoustic wave intermediate-frequency filter small, it is necessary to use a piezoelectric substrate having a low SAW velocity V, as can be appreciated from the equation (1).
For this reason, LT112 and ST quartz crystal, whose SAW velocities are low, are used for the piezoelectric substrates of surface acoustic wave intermediate-frequency filters. ST quartz crystal is particularly suitable because the primary temperature coefficient of frequency TCF is zero. Because the electromechanical coupling factor k2 of ST quartz crystal is low, only a filter having a narrow passband is achievable. However, because it is a function of the intermediate-frequency filters to pass signals through a single narrow channel, the fact that the ST quartz crystal has a small electromechanical coupling factor has caused no problem.
In recent years, however, digital mobile communication systems have been developed and put into practical use. These systems have won very rapid acceptance because of their ability to make effective use of frequency resources, compatibility with digital data communications, and so on. The passband of the digital system is very wide, for instance, several hundred KHz to several MHz. In the case where an intermediate-frequency filter having such a wide passband is constructed using a surface acoustic wave device, it is difficult to use an ST quartz crystal substrate. In order to further reduce the size of mobile communication terminals for enhanced portability, it is required to reduce the mounting area of surface acoustic wave intermediate-frequency filters. However, because the SAW velocities of ST quartz crystal and LT112, which are considered to be suitable for surface acoustic wave intermediate-frequency filters, are over 3100 m/sec, further minimization is difficult.
As explained above, when surface acoustic wave devices for intermediate-frequency are constructed using piezoelectric substrates having high electromechanical coupling factor such as 128LN, 64LN, and 36LT, the device size must be large since the SAW velocities of the substrates are high, although a wide passband can be obtained. On the other hand, when surface acoustic wave devices for intermediate-frequency are constructed using piezoelectric substrates having low SAW velocities such as ST quartz crystal and LT112 in order to reduce the device size, a wide passband cannot be obtained since the electromechanical coupling factors of the substrates are low. Thus, surface acoustic wave devices for intermediate-frequency having excellent characteristics cannot be obtained in either case.
It is therefore an object of the present invention to provide a surface acoustic wave device for intermediate-frequency enabling miniaturization and band-widening.
Another object of the present invention is to provide a piezoelectric substrate for use in a surface acoustic wave device having high electromechanical coupling factor and low SAW velocity.
The above and other objects of the present invention can be accomplished by a surface acoustic wave device comprising a piezoelectric substrate and inter-digital electrodes formed on the piezoelectric substrate, wherein: the piezoelectric substrate has a crystal structure of the Ca3Ga2Ge4O14 type and is represented by the chemical formula, Ca3TaGa3Si2O14; and a cut angle of the piezoelectric substrate cut out of the single crystal and a direction of propagation of surface acoustic waves on the piezoelectric substrate represented in terms of Euler""s angles (xcfx86, xcex8, "psgr") are found in one of a first area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa690xc2x0, and xe2x88x9265xc2x0xe2x89xa6"psgr"xe2x89xa665xc2x0, a second area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and 65xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a third area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9265xc2x0, a fourth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa690xc2x0, and xe2x88x9275xc2x0xe2x89xa6"psgr"xe2x89xa660xc2x0, a fifth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6150xc2x0, and 75xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a sixth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9260xc2x0, a seventh area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa6100xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa655xc2x0, an eighth area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6150xc2x0, and 75xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a ninth area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9255xc2x0, a tenth area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 20xc2x0xe2x89xa6xcex8xe2x89xa6105xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa650xc2x0, an eleventh area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 125xc2x0xe2x89xa6xcex8xe2x89xa6140xc2x0, and 80xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a twelfth area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 115xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9250xc2x0, a thirteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa670xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9220xc2x0, a fourteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa6110xc2x0, and xe2x88x9220xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, a fifteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 115xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9245xc2x0, a sixteenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa670xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9220xc2x0, a seventeenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa6145xc2x0, and xe2x88x9220xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, an eighteenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9240xc2x0, a nineteenth area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa670xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9230xc2x0, a twentieth area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa6150xc2x0, and xe2x88x9230xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, and a twenty-first area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9230xc2x0.
The above and other objects of the present invention can also be accomplished by a piezoelectric substrate for use in a surface acoustic wave device, characterized in that the piezoelectric substrate has a crystal structure of Ca3Ga2Ge4O14 type and is represented by the chemical formula, Ca3TaGa3Si2O14; and a cut angle of the piezoelectric substrate cut out of the single crystal and a direction of propagation of surface acoustic waves on the piezoelectric substrate represented in terms of Euler""s angles (xcfx86, xcex8, "psgr") are found in one of a first area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa690xc2x0, and xe2x88x9265xc2x0xe2x89xa6"psgr"xe2x89xa665xc2x0, a second area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and 65xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a third area represented by xe2x88x922.5xc2x0xe2x89xa6xcfx86xe2x89xa62.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9265xc2x0, a fourth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa690xc2x0, and xe2x88x9275xc2x0xe2x89xa6"psgr"xe2x89xa660xc2x0, a fifth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6150xc2x0, and 75xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a sixth area represented by 2.5xc2x0xe2x89xa6xcfx86xe2x89xa67.5xc2x0, 120xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9260xc2x0, a seventh area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa6100xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa655xc2x0, an eighth area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 120xc2x0xe2x89xa6xcex8150xc2x0, and 75xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a ninth area represented by 7.5xc2x0xe2x89xa6xcfx86xe2x89xa612.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9255xc2x0, a tenth area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 20xc2x0xe2x89xa6xcex8xe2x89xa6105xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa650xc2x0, an eleventh area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 125xc2x0xe2x89xa6xcex8xe2x89xa6140xc2x0, and 80xc2x0xe2x89xa6"psgr"xe2x89xa685xc2x0, a twelfth area represented by 12.5xc2x0xe2x89xa6xcfx86xe2x89xa617.5xc2x0, 115xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa650xc2x0, a thirteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa670xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9220xc2x0, a fourteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa6110xc2x0, and xe2x88x9220xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, a fifteenth area represented by 17.5xc2x0xe2x89xa6xcfx86xe2x89xa622.5xc2x0, 115xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9245xc2x0, a sixteenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 25xc2x0xe2x89xa6"psgr"xe2x89xa670xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9220xc2x0, a seventeenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa6145xc2x0, and xe2x88x9220xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, an eighteenth area represented by 22.5xc2x0xe2x89xa6xcfx86xe2x89xa627.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9280xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9240xc2x0, a nineteenth area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 25xc2x0xe2x89xa6xcex8xe2x89xa670xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9230xc2x0, a twentieth area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 30xc2x0xe2x89xa6xcex8xe2x89xa6150xc2x0, and xe2x88x9230xc2x0xe2x89xa6"psgr"xe2x89xa640xc2x0, and a twenty-first area represented by 27.5xc2x0xe2x89xa6xcfx86xe2x89xa632.5xc2x0, 110xc2x0xe2x89xa6xcex8xe2x89xa6155xc2x0, and xe2x88x9285xc2x0xe2x89xa6"psgr"xe2x89xa6xe2x88x9230xc2x0.
The present invention is based on the experimentally acquired knowledge that when a single crystal represented by the chemical formula, Ca3TaGa3Si2O14 (hereinafter, a single crystal including Ca, Ta, Ga, and Si is referred to as xe2x80x9can CTGS single crystalxe2x80x9d) has a specifically combined cut angle and direction of propagation of surface acoustic waves such that when represented by xcfx86, xcex8, and "psgr" in terms of Euler""s angles (xcfx86, xcex8, "psgr"), they are present within the first area to the twenty-first area, such properties as expressed in terms of a SAW velocity of less than 3100 m/s and an electromechanical coupling factor of greater than 0.2% can be obtained.
The present invention is intended to achieve a surface acoustic wave device having excellent characteristics by employing an CTGS single crystal as the substrate of the surface acoustic wave device and selecting the cut angle of the crystal and the direction of propagation of surface acoustic waves within a specific range.
In the present invention, the CTGS crystal is most preferably Ca3TaGa3Si2O14. However, the composition ratios between the respective elements may be slightly varied insofar as the technical advantages of the present invention are not diminished. Further, the CTGS single crystal may contain unavoidable impurities such as Al, Zr, Fe, Ce, Nd and Pt. Furthermore, the CTGS single crystal may contain oxygen defects. The method of manufacturing the CTGS single crystal is not particularly limited. An ordinary crystal growing process such as the CZ process can be employed for manufacturing the CTGS single crystal.
It is to be noted that the CTGS single crystal is a trigonal system, and so mutually equivalent combinations of Euler""s angles exist due to crystal symmetry. In the trigonal system substrate, xcfx86=120xc2x0 to 240xc2x0 and xcfx86=240xc2x0 to 360xc2x0 (xe2x88x92120xc2x0 to 0xc2x0) are equivalent to xcfx86=0xc2x0 to 120xc2x0; xcex8=360xc2x0 to 180xc2x0 (0xc2x0 to xe2x88x92180xc2x0) is equivalent to xcex8=0xc2x0 to 180xc2x0; and "psgr"=270xc2x0 to 90xc2x0 is equivalent to "psgr"=xe2x88x9290xc2x0 to 90xc2x0. For example, xcfx86=130xc2x0 and xcfx86=250xc2x0 are equivalent to xcfx86=10xc2x0; xcex8=330xc2x0 is equivalent to xcex8=30xc2x0; and "psgr"=240xc2x0 is equivalent to "psgr"=60xc2x0.
Further, in the trigonal system substrate, the characteristics thereof at all cut angles and in all propagation directions can be learned by determining the characteristics in the range of xcfx86 from 0xc2x0 to 30xc2x0.
Therefore, in order to learn the characteristics thereof at all cut angles and in all propagation directions, it is sufficient to study the characteristics thereof only in the range of xcfx860=0xc2x0 to 30xc2x0 s, xcex80=0xc2x0 to 180xc2x0 and "psgr"0=xe2x88x9290xc2x0 to 90xc2x0. Based on the combination (xcfx860, xcex80, "psgr"0), an equivalent combination exhibiting the same characteristics in the range of xcfx86=30xc2x0 to 120xc2x0 can be learned. Concretely, in the range of 30xc2x0xe2x89xa6xcfx86xe2x89xa660xc2x0, (xcfx86, xcex8, "psgr") equivalent to (xcfx860, xcex80, "psgr"0) can be obtained by xcfx86=60xc2x0xe2x88x92xcfx860, xcex8=180xc2x0xe2x88x92xcex80 and "psgr"="psgr"0; in the range of 60xc2x0xe2x89xa6xcfx86xe2x89xa690xc2x0, (xcfx86, xcex8, "psgr") equivalent to (xcfx860, xcex80, "psgr"0) can be obtained by xcfx86=60xc2x0+xcfx860, xcex8=180xc2x0xe2x88x92xcex80 and "psgr"=xe2x88x92"psgr"0; and in the range of 90xc2x0xe2x89xa6xcfx86xe2x89xa6120xc2x0, (xcfx86, xcex8, "psgr") equivalent to (xcfx860, xcex80, "psgr"0) can be obtained by xcfx86=120xc2x0xe2x88x92xcfx860, xcex8=xcex80 and "psgr"=xe2x88x92"psgr"0. As a result, based on the aforementioned symmetrical property, the characteristics of the CTGS single crystal substrate for all (xcfx86, xcex8, "psgr") can be learned.
Set out below are exemplary equivalent combinations.
Equivalent to (0xc2x0, 140xc2x0, 25xc2x0) are (60xc2x0, 40xc2x0, 25xc2x0), (60xc2x0, 40xc2x0, xe2x88x9225xc2x0) and (120xc2x0, 140xc2x0, xe2x88x9225xc2x0) and since xcfx86=120xc2x0 is equivalent to xcfx86=0xc2x0, (0xc2x0, 140xc2x0, xe2x88x9225xc2x0) is also equivalent to (0xc2x0, 140xc2x0, 25xc2x0).
The first area to the twenty-first area include all combinations of equivalent (xcfx86, xcex8, "psgr") obtained in the above described manner.
In general, the surface acoustic wave device according to the present invention lends itself well to filters used in the frequency band of 10 to 500 MHz particularly, 10 to 300 MHz.
Further, the surface acoustic wave device according to the present invention is also useful for making a surface acoustic wave delay element small, because of the low SAW velocity thereof.